Works at the Gate Lodge in Castleblayney are expected to be completed by the end of the year.
The contractor has installed a steel frame and works are progressing for the floor levels.
The rebuilding of the stone boundary wall and the installation of foundations for an extension are said to be substantially complete.
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When finished, the building will house a new state-of-the-art library.
Works are scheduled to be completed in the latter part of 2022.